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A critical problem associated with surgical simulation is balancing deformation accuracy with a real-time performance. Although the canonical surface mass-spring model (MSM) can provide an excellent real-time performance, it fails to provide effective shape restoration behavior when generating large deformations. This significantly influences its deformation accuracy. To address this problem, this paper proposes a modified surface MSM. In the proposed MSM, a new flexion spring is first developed to oppose bending based on the included angle between the initial position vector and the deformational position vector, improving the shape restoration performance, and enhance the deformational accuracy of MSM; then, a new type of surface triangular topological unit is developed for enhancing the computational efficiency and better adapting to the different topological soft tissue deformational models. In addition, to further improve the accuracy of deformational interactions between the soft tissue and surgical instruments, we also propose two new collision detection algorithms. One is the discrete collision detection with the volumetric structure (DCDVS), applying a volumetric structure to extend the effective range of collision detection and the other is the hybrid collision detection with the volumetric structure (HCDVS), introducing the interpolation techniques of the continuous collision detection to DCDVS. Experimental results show that the proposed MSM with the DCDVS or the HCDVS can achieve accurate and stable shape restoration and show the real-time interactive capability in the virtual artery vessel and heart compared with the canonical surface MSM and new volume MSM.

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A Surface Mass-Spring Model With New Flexion Springs and Collision Detection Algorithms Based on Volume Structure for Real-Time Soft-Tissue Deformation Interaction